In the prior art of digital radio communication, it is well known that linearly filtered transmissions can achieve superior spectral containment, thus reducing adjacent channel interference. Linearly filtered transmissions may be produced according to the prior art by applying information-symbol-representative impulses to a premodulation filter of desired characteristics. Such impulses, in the case of binary symbols, are impulses of area either +1 or −1. In the case of complex modulation, which produces both variations of the signal phase and amplitude creating a time-varying signal vector in the two-dimensional complex plane, the symbol-representative impulses have both a real (x or In-phase) part usually denoted by Ii, and an imaginary (y or Quadrature) part denoted by Qi. The complex symbol Si=Ii+jQi may be filtered by separately filtering the I and Q sequences.
It is also known in the prior art that filtering may be performed using Finite Impulse Response (FIR) filters, which perform a weighted sum over the sliding window of successive symbols. Recent innovations in FIR filters are disclosed in U.S. Pat. No. 5,867,537 to Applicant, which is hereby incorporated by reference.
Also in the prior art, it is known that all possible output values of an FIR filter may be precomputed and stored in a look-up table, providing the number of symbols L over the sliding FIR filter window is not too large. The number of stored output waveforms must be ML when using symbols selected from an alphabet of M possible values. To reduce this number, U.S. Pat. No. 5,867,537 to Applicant splits the look-up table into two tables, each addressed by L/2 symbols. When M is large, for example 8 in an exemplary implementation, the size of the look-up table can nevertheless be excessive. Therefore, there is a need to reduce the size of look-up tables for generating filtered modulation waveforms for 8-PSK and similar modulations.